Data exploration and summarization are essential steps in any experimental design, as they help you understand the characteristics, patterns, and relationships in your data. In this article, you will learn how to use graphical and numerical methods to explore and summarize your data, and what to look for in each method.
Graphical methods are visual representations of your data, such as histograms, box plots, scatter plots, and bar charts. They can help you identify the distribution, shape, outliers, trends, and clusters in your data. For example, a histogram can show you the frequency of values in a variable, a box plot can show you the median, quartiles, and extreme values, a scatter plot can show you the correlation and linearity between two variables, and a bar chart can show you the counts or proportions of categories in a variable. To use graphical methods, you need to select the appropriate type of plot for your data type and question, and use software tools or libraries such as Excel, R, or Python to create and customize your plots.
You should expect to produce lots of plots for any given data as you start to work with it. You won't know in advance what the data holds, and every plot gives just one view. Even if only considering histograms, you might try many variations in bin size, subsets, and transforms of the data. It's worth differentiating the many plots you make for yourself from the relatively small number of plots you might make to share with others. You might make a hundred quick plots, but produce just a single refined and likely simplified plot to communicate an important finding.
Numerical methods are quantitative measures of your data, such as mean, median, mode, standard deviation, range, quartiles, correlation, and p-value. They can help you summarize the central tendency, variability, skewness, and significance of your data. For example, the mean can show you the average value of a variable, the standard deviation can show you the spread of values around the mean, the skewness can show you the asymmetry of the distribution, and the p-value can show you the probability of observing a result by chance. To use numerical methods, you need to calculate the relevant statistics for your data using formulas, software tools, or libraries, and interpret them in relation to your hypothesis and research question.
Numerical summaries are almost always quite "lossy" compared to good graphical methods: you lose a lot of information to get to one or a few numbers for a whole dataset. This can be useful, but be aware of the tradeoff.
Exploratory data analysis (EDA) is the process of using graphical and numerical methods to explore your data before conducting formal statistical tests or modeling. This approach can help you check the quality and validity of your data, identify potential problems or errors, discover interesting patterns or insights, and generate hypotheses or questions for further analysis. To perform EDA correctly, you must follow a systematic and iterative approach, such as defining your research question and objectives, importing and inspecting your data, cleaning and transforming it, visualizing and summarizing it, as well as analyzing and interpreting it.
It is important to be consistent and iterative in both the exploratory phase and the reporting phase of every project. Although each dataset will require different visualization strategies, it is important to keep the visualization methods and parameters consistent and tailored to your audience, especially when working on the same project, and to keep track of how visualizations are built. More often than not, we get lost in the data and forget how important it is to record every step of the analytic process. Not doing so can ultimately delay projects and introduce inconsistencies and biases on the data.
Confirmatory data analysis (CDA) is the process of using graphical and numerical methods to test hypotheses or answer research questions using formal statistical tests or modeling. This approach can help you confirm or reject hypotheses, estimate effect size and confidence interval, and evaluate the assumptions and limitations of your analysis. To perform CDA, you must take a rigorous and objective approach. This includes choosing the appropriate statistical test or model for your data type and question, applying the test or model to the data, checking the assumptions and conditions of the test or model, reporting and interpreting the results and conclusions, and communicating and visualizing your findings.
Graphical and numerical methods are complementary and not mutually exclusive, as they can provide different perspectives and information on your data. Graphical methods are more intuitive and exploratory, as they can reveal patterns and outliers that may not be evident from numerical methods. Numerical methods are more precise and confirmatory, as they can quantify and test the significance and uncertainty of your data. Therefore, it is recommended to use both graphical and numerical methods in your data analysis, and to compare and contrast them to ensure consistency and validity.
When it comes to data analysis, graphical and numerical methods should be used effectively and ethically. The most appropriate and informative methods should be chosen for the data type and question. Labels, titles, legends, scales, and colors should be clear and consistent in plots. Misleading or distorted plots should be avoided as they can misrepresent or exaggerate your data. Descriptive and inferential statistics should be employed appropriately and cautiously, avoiding common errors such as confusion between correlation and causation, misuse of p-values, and ignoring confounding factors. Finally, results should be reported and interpreted honestly and transparently while acknowledging the limitations and assumptions of the analysis.